Question

in the figure , AB, BC and AC are tangents to the circle at P,Q and R. if AB=AC are tangents to the circle at P,Q and R. show that Q is the midpoint of BC ​

Answer 1

Answer:

Step-by-step explanation:

AP=AR...(1)

PB=BQ...(2)

RC=QC...(3)

ITS GIVEN THAT AB=AC

AP+PB=AR+RC

PUTTING VALUE OF AP

AR+PB=AR+RC

PB=RC

PUTTING VALUE FROM EQ 2 N 3

WE GET,

BQ=QC

HENCE,Q IS THE MID POINT

MARK IT AS BRAINLIST PLSS

Answer 2

Answer:

The proof is explained below.

Step-by-step explanation:

Given AB, BC and AC are tangents to the circle at P,Q and R. if AB=AC are tangents to the circle at P,Q and R.

we have to prove that  Q is the midpoint of BC

i.e BQ=QC

By the theorem which states that if two different tangents are drawn to the same circle at a common point, the distance between that point and the two points of tangency are the equal.

AP=AR...(1)

PB=BQ...(2)

RC=QC...(3)

It is given that  AB=AC

AP+PB=AR+RC

AP+PB=AP+RC      (∵ From 1)

PB=RC

From eq (2) and (3), we get

BQ=QC

Hence, Q is the mid-point.